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Sequential Estimation of Structural Models with a Fixed Point Constraint

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  • Kasahara, Hiroyuki
  • Shimotsu, Katsumi

Abstract

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze the conditions under which the nested pseudo-likelihood (NPL) algorithm achieves convergence and derive its convergence rate. We find that the NPL algorithm may not necessarily converge when the fixed point mapping does not have a local contraction property. To address the issue of non-convergence, we propose alternative sequential estimation procedures that can achieve convergence even when the NPL algorithm does not. Upon convergence, some of our proposed estimation algorithms produce more efficient estimators than the NPL estimator.
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Suggested Citation

  • Kasahara, Hiroyuki & Shimotsu, Katsumi, 2009. "Sequential Estimation of Structural Models with a Fixed Point Constraint," Discussion Papers 2009-18, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2009-18
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    2. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    3. Victor Aguirregabiria & Mathieu Marcoux, 2021. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Quantitative Economics, Econometric Society, vol. 12(4), pages 1223-1271, November.
    4. Adam Dearing & Jason R. Blevins, 2019. "Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games," Papers 1912.10488, arXiv.org, revised Feb 2021.
    5. Taisuke Otsu & Martin Pesendorfer & Yuya Takahashi, 2016. "Pooling data across markets in dynamic Markov games," Quantitative Economics, Econometric Society, vol. 7(2), pages 523-559, July.
    6. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2013. "Testing for equilibrium multiplicity in dynamic Markov games," LSE Research Online Documents on Economics 101968, London School of Economics and Political Science, LSE Library.
    7. Christopher Ferrall, 2020. "Object Oriented (Dynamic) Programming: Replication, Innovation and "Structural" Estimation," Working Paper 1432, Economics Department, Queen's University.
    8. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    9. Taisuke Otsu & Martin Pesendorfer, 2021. "Equilibrium multiplicity in dynamic games: testing and estimation," STICERD - Econometrics Paper Series 618, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    11. Liu, Xiaodong & Zhou, Jiannan, 2017. "A social interaction model with ordered choices," Economics Letters, Elsevier, vol. 161(C), pages 86-89.
    12. Fabio A. Miessi Sanches & Daniel Junior Silva & Sorawoot Srisuma, 2016. "Ordinary Least Squares Estimation Of A Dynamic Game Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(2), pages 623-634, May.
    13. Marleen Marra, 2019. "Pricing and Fees in Auction Platforms with Two-Sided Entry," Working Papers hal-03393068, HAL.
    14. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    15. Jinhyuk Lee & Kyoungwon Seo, 2015. "A computationally fast estimator for random coefficients logit demand models using aggregate data," RAND Journal of Economics, RAND Corporation, vol. 46(1), pages 86-102, March.
    16. Sumon Datta & K. Sudhir, 2012. "Does Reducing Spatial Differentiation Increase Product Differentiation" Effects of Zoning on Retail Entry and Format Variety," Cowles Foundation Discussion Papers 1851, Cowles Foundation for Research in Economics, Yale University, revised Sep 2012.
    17. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.
    18. Sumon Datta & K. Sudhir, 2013. "Does reducing spatial differentiation increase product differentiation? Effects of zoning on retail entry and format variety," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 83-116, March.
    19. Marleen Marra, 2019. "Pricing and Fees in Auction Platforms with Two-Sided Entry," Sciences Po Economics Discussion Papers 2020-02, Sciences Po Departement of Economics.
    20. Jason R. Blevins & Minhae Kim, 2021. "Nested Pseudo Likelihood Estimation of Continuous-Time Dynamic Discrete Games," Papers 2108.02182, arXiv.org.
    21. Chomsisengphet, Souphala & Kiefer, Hua & Liu, Xiaodong, 2018. "Spillover effects in home mortgage defaults: Identifying the power neighbor," Regional Science and Urban Economics, Elsevier, vol. 73(C), pages 68-82.
    22. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    23. Sun, Yutec & Ishihara, Masakazu, 2019. "A computationally efficient fixed point approach to dynamic structural demand estimation," Journal of Econometrics, Elsevier, vol. 208(2), pages 563-584.
    24. José-Alberto Guerra & Myra Mohnen, 2017. "Multinomial choice with social interactions: occupations in Victorian London," Documentos CEDE 015667, Universidad de los Andes - CEDE.
    25. Marleen Marra, 2019. "Pricing and Fees in Auction Platforms with Two-Sided Entry," Sciences Po publications 2020-02, Sciences Po.

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    More about this item

    Keywords

    contraction; dynamic games; nested pseudo likelihood; recursive projection method;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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